Given a quantum evolution \(U_{AB}:\mathcal {H}_A\otimes \mathcal {H}_B\rightarrow \mathcal {H}_C\otimes \mathcal {H}_D\) ,
we consider a state representation of \(U_{AB}\)  by augmenting reference states on \(\mathcal {H}_R\)  and \(\mathcal {H}_{B^{\prime }}\)  [1]}:
\({\Psi } = (I_{R}\otimes U_{AB}\otimes I_{B^{\prime }})({\text{EPR}}_{RA}\otimes {\text{EPR}}_{BB^{\prime }})={\begin{array}{c}\vbox {\vspace{1.19998pt}\hbox{\hspace{0.79999pt}\includegraphics [scale=0.4]{fig_HPstate}}}\end{array}},\) 
